Fast and stable manipulation of a charged particle in a Penning trap

Kiely, Anthony; McGuinness, J P L; Muga, J. G.; Ruschhaupt, A.

doi:10.1088/0953-4075/48/7/075503

Cited by 30 publications

(42 citation statements)

References 34 publications

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“…Such shortcuts are fast processes with suppressed nonequilibrium excess energy [2,3], and apparently provide means to circumvent the second law in isolated systems [4][5][6]. Thus, a variety of techniques has been developed: using dynamical invariants [7], inversion of scaling laws [8], the fast-forward technique for Schrödinger [9][10][11][12][13][14] and Dirac dynamics [15], transitionless quantum driving [16][17][18][19], classical dissipationless driving [20,21], optimal protocols from optimal control theory [22][23][24][25][26][27][28], optimal driving from properties of the quantum work statistics [29], 'environment' assisted methods [30], using the properties of Lie algebras [31], and approximate methods such as linear response theory [5] and fast quasistatic dynamics [32].Among this plethora of techniques transitionless quantum driving (TQD) is unique. In its original formulation [16-18] one considers a time-dependent Hamiltonian H 0 (t) and constructs an additional counterdiabatic field, H 1 (t), such that the joint Hamiltonian H(t) = H 0 (t) + H 1 (t) drives the dynamics precisely through the adiabatic manifold of H 0 (t).…”

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confidence: 99%

Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity

2017

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Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics.Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous link between this speed, the quantum speed limit, and the (energetic) cost of implementing such a shortcut to adiabaticity. Interestingly, this link elucidates a trade-off between speed and cost, namely that instantaneous manipulation is impossible as it requires an infinite cost. These findings are illustrated for two experimentally relevant systems -the parametric oscillator and the Landau-Zener model -which reveal that the spectral gap governs the quantum speed limit as well as the cost for realizing the shortcut.

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confidence: 99%

Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity

2017

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“…The electromagnetic field investigated in Refs. [3,19] was not used to suppress the additional phase.…”

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confidence: 99%

Fast forward of adiabatic control of tunneling states

et al. 2017

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By developing the preceding work on the fast forward of transient phenomena of quantum tunneling by Khujakulov and Nakamura (Phys. Rev. {\bf A 93}, 022101 (2016) ), we propose a scheme of the exact fast forward of adiabatic control of stationary tunneling states with use of the electromagnetic field. The idea allows the acceleration of both the amplitude and phase of wave functions throughout the fast-forward time range. The scheme realizes the fast-forward observation of the transport coefficients under the adiabatically-changing barrier with the fixed energy of an incoming particle. As typical examples we choose systems with (1) Eckart's potential with tunable asymmetry and (2) double $\delta$-function barriers under tunable relative height. We elucidate the driving electric field to guarantee the stationary tunneling state during a rapid change of the barrier and evaluate both the electric-field-induced temporary deviation of transport coefficients from their stationary values and the modulation of the phase of complex scattering coefficientsComment: 15 pages, 8 figure

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“…Thus, to circumvent, mitigate, and suppress such finite-time excitations in controlled quantum processes, a wide variety of techniques has been developed. Among the most successful approaches are transitionless quantum driving [ 9 , 10 , 11 , 12 , 13 ], the fast-forward technique [ 14 , 15 , 16 , 17 ], and methods that rely on identifying the adiabatic invariants [ 18 , 19 , 20 , 21 ], to name just a few. For a comprehensive exposition of the field “shortcuts to adiabaticity”, we refer to recent reviews [ 22 , 23 ], a special collection of articles [ 24 ], and a perspective [ 25 ].…”

Section: Introductionmentioning

confidence: 99%

Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals

Roychowdhury

Deffner

2021

Entropy

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Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame, the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.

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Fast and stable manipulation of a charged particle in a Penning trap

Cited by 30 publications

References 34 publications

Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity

Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity

Fast forward of adiabatic control of tunneling states

Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals

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